¥3,500,000 (Direct Cost: ¥3,500,000)

Based on analogies between knots and primes, I investigated the connection and interaction between knot theory and number theory. In this year, my concern has been focused on the following topics :I showed the analogy between the structure of the deformation space of hyperbolise structures on a knot complement and the deformation space of p-adic Galvis representations of a prime group. Based on this analogy, I discussed some analogous features between the variation of Sh_2(C) Chern-Simons. in variants and p-adre modulus L-function. In particular, I gave an interpretation of the Chern-Simons invariant in terms of Deligne cohomology, Jointly with Y.Terashima. I talked about Dnr results in the international conferees hold at Hiroshima Univ.(2006,July), Max Plank Inst.(2006,Sept) and Kyoto Un.(2006,Dec)